The thesis deals with sensor networks and their localization. First section describes sensor networks in general and explains problems of localization and routing. The second part deals with localization using anchors. The principal of the Dv-hop and DV-Distance are there described in detail. These algorithms are used for simulations in Matlab in the main part of this thesis. According to the simulations the most sufficient number of sensors for good localization is estimated.

<p>U doktorskoj disertaciji obrađen je problem upravljanja montažnim<br />sistemima pomoću bežične senzorske tehnologije u cilju poboljšanja<br />efikasnosti proizvodnje i poboljšanja kvaliteta proizvoda. U okviru<br />ove disertacije je razvijen model bežičnog upravljačkog sistema za<br />upravljanje i nadzor industrijskih procesa. Glavni cilj istraživanja<br />je razvoj integrisanog sistema za praćenje pozicije radnog predmeta i<br />praćenje okolnosti u kojima se radni predmet nalazi u montažnim<br />sistemima. Rezultati istraživanja su potvrđeni eksperimentalnim<br />istraživanjem u laboratorijskoj i u realnoj industrijskoj sredini.</p> / <p>The dissertation deals with the problem of monitoring and controlling<br />industrial assembly lines by wireless sensor technology with the aim of<br />improving the efficiency of production and the quality of the product. A model<br />of a wireless controlling system has been developed for monitoring and<br />controlling industrial processes. The main focus of the study is the<br />development of an integrated system for monitoring the position of the<br />product and the influences on the product in the assembly lines. The results<br />are confirmed by experiments in a laboratory and real industrial environment.</p>

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The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

Advancement of micro-electro-mechanics and wireless communication have proliferated the deployment of large-scale wireless sensor networks. Due to cost, size and power constraints, at most a few sensor nodes can be equipped with a global positioning system; such nodes (whose positions can be accurately determined) are referred to as anchors. However, one can deter-mine the distance between two nearby sensors using some form of local communication. The problem of computing the positions of the non-anchor nodes from the inter-sensor distances and anchor positions is referred as sensor network localization (SNL). In this dissertation, our aim is to develop an accurate, efficient, and scalable localization algorithm, which can operate both in the presence and absence of anchors. It has been demon-strated in the literature that divide-and-conquer approaches can be used to localize large net-works without compromising the localization accuracy. The core idea with such approaches is to partition the network into overlapping subnetworks, localize each subnetwork using the available distances (and anchor positions), and finally register the subnetworks in a single coordinate system. In this regard, the contributions of this dissertation are as follows: We study the global registration problem and formulate a necessary “rigidity” condition for uniquely recovering the global sensor locations. In particular, we present a method for efficiently testing rigidity, and a heuristic for augmenting the partitioned network to enforce rigidity. We present a mechanism for partitioning the network into smaller subnetworks using cliques. Each clique is efficiently localized using multidimensional scaling. Finally, we use a recently proposed semidefinite program (SDP) to register the localized subnetworks. We develop a scalable ADMM solver for the SDP in question. We present simulation results on random and structured networks to demonstrate the pro-posed methods perform better than state-of-the-art methods in terms of run-time, accuracy, and scalability.